We consider k-factorizations of the complete graph that are 1-rotational under an assigned group G, namely that admit G as an automorphism group acting sharply transitively on all but one vertex. After proving that the k-factors of such a factorization are pairwise isomorphic, we focus our attention to the special case of k = 2, a case in which we prove that the involutions of G necessarily form a unique conjugacy class. We completely characterize, in particular, the 2-factorizations that are 1-rotational under a dihedral group. Finally, we get infinite new classes of previously unknown solutions to the Oberwolfach problem via some direct and recursive constructions.

1-rotational k-factorizations of the complete graph and new solutions to the Oberwolfach Problem / Buratti, Marco; Rinaldi, G.. - In: JOURNAL OF COMBINATORIAL DESIGNS. - ISSN 1063-8539. - 16:(2008), pp. 87-100.

1-rotational k-factorizations of the complete graph and new solutions to the Oberwolfach Problem

BURATTI, Marco;
2008

Abstract

We consider k-factorizations of the complete graph that are 1-rotational under an assigned group G, namely that admit G as an automorphism group acting sharply transitively on all but one vertex. After proving that the k-factors of such a factorization are pairwise isomorphic, we focus our attention to the special case of k = 2, a case in which we prove that the involutions of G necessarily form a unique conjugacy class. We completely characterize, in particular, the 2-factorizations that are 1-rotational under a dihedral group. Finally, we get infinite new classes of previously unknown solutions to the Oberwolfach problem via some direct and recursive constructions.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1654601
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